“The Ongoing Gender Gap in Art Museum Directorships” shows that just one of the nation’s 13 largest museums is run by a woman. The report is a follow-up to a 2014 study, the first to analyze salary data collected from the association’s 200-plus membership from the vantage point of gender.

Women today are nearing equity over all, leading 48 percent of art museums, up from 43 percent three years ago. A gender gap persists, however, at the largest museums — those with budgets of $15 million and higher, where just 30 percent have female directors. And as the budgets grow, the ranks of women thin, with just three women heading the 20 largest-budget institutions in the association.

“The first step in addressing inequality is acknowledging it,” said Lisa Phillips, director of the New Museum in New York, who initiated the 2014 study and consulted on the new report. “Hard data makes it plain and clear.”

She called the 2014 report a “necessary benchmark” that gave her colleagues ammunition in salary negotiations. The new data reflects an uptick of 5 percent from three years ago in female directors’ pay at the biggest museums. But they still make only 75 cents to every dollar earned by their male peers, which lags the national average for working women by 5 percent.

The report, written in partnership with the National Center for Arts Research, attributes the gender gap to factors ranging from the age and gender of the board members hiring directors to the female candidates themselves, who may be opting out of pursuing the biggest jobs for family reasons or because of satisfaction with their current institutions.

Anne Pasternak joined the top tier of the 20 largest museums when she was hired as director of the Brooklyn Museum in 2015. She had previously led the small, innovative organization Creative Time and was widely seen as an unexpected but exciting choice. Sarah James of Phillips Oppenheim, the executive recruiting firm that led the search, said the decision required the Brooklyn board to see beyond the fact that Ms. Pasternak hadn’t run a large-scale institution, or an encyclopedic museum, before.

“The board was really captivated with how she did so well in building Creative Time, the markets that she played to with that organization and the attention to diversity she paid,” Ms. James said. They decided they could “hire the management side if she needed help.” The vote was unanimous, but it probably didn’t hurt that the Brooklyn Museum had a female board chair, a female vice chair and two female search committee chairs.

The study does show that women now run 54 percent of the small and midsize museums with budgets under $15 million and make almost equal pay in those jobs as men, just 2 percent less. “It will be interesting to see where those directors go,” said Christine Anagnos, executive director of the association, “if what we’re seeing is the building of a pipeline” to the larger jobs.

While most boards ask for a diverse slate of candidates at the start of a search, Ms. James has observed reticence in discussing gender and race head-on. “I think people are still scared to engage in the conversation around diversity and what it means because they don’t trust themselves to step in it,” she said. “They just keep quiet, and when you keep quiet, you can’t make progress.”

“It’s not an insurmountable thing in the world for a woman to run a major museum,” Ms. Easton said. “Witness the recent appointments of Maria Balshaw to the Tate museums in Britain, where Frances Morris is already the director of Tate Modern, and Laurence des Cars to the Musée d’Orsay in Paris.”

If a woman were to break the “ultimate glass ceiling” at the Met, she added, “it would help reduce the unthinking bias against women at the top of other large institutions.”

The Metropolitan Museum has yet to form a search committee.

Beyond issues of equity and symbolism, would it make a difference qualitatively if a woman were to get the job?

“Museums are incredibly complex organizations where the director is the artistic visionary, the manager of people and finances, the board liaison and the fund-raiser,” Ms. Fogarty said. “More institutions are having to find a collective leadership structure.” Based on her own experiences, she added, “That’s something that many women seem to be comfortable with — and actually want to promote.”

A version of this article appears in print on , on Page C3 of the New York edition with the headline: Study Finds Persistent Museum Gender Gap. Order Reprints | Today’s Paper | Subscribe